Method and Device for Determining Fouling in a Heat Exchanger

ABSTRACT

A device and method for increasing accuracy in the determination of fouling in a heat exchanger in which heat is transferred from a first medium to a second medium, wherein a value for a variable characterizing the fouling is determined from a value for a first variable influenced by the fouling and a value for a second variable, where the second variable compensates for a change in the first variable caused by a change in flow of the first and/or second mediums through the heat exchanger, where the first variable can be a thermal transmission resistance, a thermal transmittance or a thermal transmission coefficient, where the first and second variable are determined from values measured totemperaturesr and flows of the first and second mediums without using material properties of the first and second mediums and structural properties of the heat exchanger when determining the first and second variables.

CROSS-REFERENCE TO RELATED APPLICATIONS

This is a U.S. national stage of application No. PCT/EP2021/055563 filed5 Mar. 2021. Priority is claimed on European Application No. 20161837.8filed 9 Mar. 2010, the content of which is incorporated herein byreference in its entirety.

BACKGROUND OF THE INVENTION 1. Field of the Invention

The invention relates to a method and a device for determining foulingin a heat exchanger.

2. Description of the Related Art

Heat exchangers are technical apparatuses used to heat or cool a medium.To this end, heat is transferred from a warmer first medium to a coolersecond medium. Depending on their construction, heat exchangers differin their functional principle. The most frequent constructions areclassified into one of three function groups: direct current, reversecurrent or cross-flow heat exchangers.

The medium to be heated or cooled is frequently also referred to as“product medium” and the heating or cooling medium is frequently alsoreferred to as “service medium”. The service medium can be heating steamor cooling water, for example. The service medium normally flows eitherthrough an arrangement of lines that is arranged inside the productmedium, or flows around an arrangement of lines through which theproduct medium flows.

The first and the second medium are conducted through the heatexchanger, where both the media normally flow past one another,separated by a wall, and thereby the heat of the warmer medium isdissipated to the colder medium through the wall.

A key problem with heat exchangers is represented by what is known as“fouling”, in which deposits or coatings form on the inner walls of theheat exchanger. The reasons why such deposits occur may be of aphysical, chemical or biological nature. In many cases, it is notpossible to prevent them, for example, because of the given basicproduct-related conditions. The coatings impede the thermal transmissionbetween the media and thereby reduce the efficiency of the heatexchanger. Once a particular degree of contamination is reached,chemical or mechanical cleaning is necessary, or where appropriate theheat exchanger may even need to be replaced. This problem isparticularly prevalent in the case of large industrial heat exchangersthat are employed in process engineering plants (i.e., for example,plants in the chemical, petrochemical, glass, paper, metal production orcement industries) or in power plants, where they are normally designedfor a thermal transmission capacity of more than 100 kW.

From the outside, it is very difficult to determine the extent of thecontamination in the interior of the heat exchanger, so that it is notpossible to clean or replace the heat exchanger based on need. Atemperature control circuit can to a certain extent compensate for theeffects of the contamination, so that the contamination is notimmediately apparent from the outlet temperature of the product medium.Because of this lack of knowledge, it is frequently not possible toclean or replace the heat exchanger based on need.

Until now, heat exchangers affected by contamination have therefore beencleaned or replaced at regular intervals, i.e., without knowing theactual state of contamination. In this procedure, the maintenanceintervals cannot be adjusted as a function of different degrees ofcontamination. Consequently, the heat exchanger may, for example, becleaned or replaced too early, even though only minor deposits arepresent up to this point. Although this would ensure the efficientoperation of the heat exchanger, it would however be uneconomical,because not only are direct costs for the maintenance work incurred, butalso indirect costs because of the additional adverse effect on theongoing operation of the plant in which the heat exchanger is employed.If corresponding measures are taken too late, excess deposits in theinterior of the heat exchanger already result in a significantly reducedthermal transmission. The consequence is that for the same heat flow tobe transmitted a much larger flow of the service medium is required thanis the case when the heat exchanger is in a clean state. This results inan increased energy input that is expended for the provision of theservice medium, i.e., heat output and pumping capacity, which likewiserepresents a cost factor. Furthermore, when there is a heavy formationof deposits there is also the risk that the quality of the productmedium will be impaired, because specified temperatures cannot beappropriately adhered to, for example.

EP 2 128 551 Al discloses a method for monitoring the effectiveness of aheat exchanger with respect to fouling, in which a current heat flow{dot over (Q)}_(P) of the product medium or {dot over (Q)}_(s) of theservice medium is detected and compared with at least one reference heatflow {dot over (Q)}_(Ref) that corresponds to a predetermined degree ofcontamination, for example, the zero degree of contamination and amaximum permitted degree of contamination, of the heat exchanger. Therespective reference heat flow {dot over (Q)}_(Ref) is determined as afunction of the current operating point of the heat exchanger from acharacteristic field previously created and stored with the help of asimulation program for different operating points, where the operatingpoint of the heat exchanger is determined by the flows F_(P), F_(s) ofboth media and their temperatures T_(P, In), T_(S, In) on entry into theheat exchanger. By using the simulation program, the operating pointdependency of the transferrable amount of heat can, for example, beprecalculated at several hundred interpolation points, without having toperform correspondingly time-consuming measurements in the real plant.

WO 2019/001683 A1 discloses a method for monitoring a heat exchanger, inwhich the flows, inlet temperatures and outlet temperatures of serviceand product medium represent process variables, at least one processvariable of which is variable on the product side and the inlettemperature is fixed on the service side and the remaining processvariables are variable. In order to monitor the heat exchanger withoutmeasuring the temperature on the service side, the variable processvariable(s) of the product medium and the flow of the service medium aremeasured, and a characteristic field for the mutual dependence of thevariable process variable(s) of the product medium and of the flow ofthe service medium is ascertained from the measured values obtained inthis case in a reference state of the heat exchanger, and is stored. Forthe measured values obtained in a current unknown state of the heatexchanger, a distance of the measured value tuple formed from themeasured values to the characteristic field is ascertained as ameasurement of the deviation of the current state of the heat exchangerfrom the reference state.

From Zölzer K et al. “Application of the boiler diagnosis system KEDI atStaudinger 5 power station”, VGB Kraftwerkstechnik, Essen, Germany, Vol.75, No. 9, 1 September 1995, pages 755-762, ISSN: 0372-5715, and from DE195 02 096 Al, US 4 390 058 A or EP 0 470 676 A2 it is known for thethermal transmission coefficient or k value to be taken intoconsideration when monitoring heat exchangers. The heat flow {dot over(Q)}=k·A·OT_(M) transferred within the heat exchanger depends on this kvalue, on the exchange surface A and on what is known as the logarithmictemperature difference ΔT_(m) driving the thermal transmission. Both thek value and the logarithmic temperature difference are each dependent onthe operating point of the heat exchanger and thus on the flows F_(P),F_(s) of the product and service medium and their temperaturesT_(P, In), T_(S, In) on entry into the heat exchanger.

In the case of DE 195 02 096 A1, a current K value is determined foreach heating surface from a calculated heat output, a logarithmictemperature difference and the size of the heating surface. By comparingthe current K value with a stored reference K value Kref for the“cleanest possible state”, a cleaning state CF is calculated inaccordance with the relationship CF=K/Kref. The reference values Krefare stored in a memory as a function of the load and possibly as afunction of the fuel. The reference values Kref can be corrected usingcorrection factors in accordance with certain current state variables.Thus, for example, a correction is performed in accordance with thesteam velocity. However, how the reference values are obtained remainsan open question.

In the case of Zolzer, a “heating surface valency FV” is defined as ameasurement for heating surface contamination. This is defined as theratio of an actual evaluation factor factual to a base evaluation factorfbase. The actual evaluation factor factual is the ratio of a “measured”thermal transmission coefficient Kactual to a theoretical thermaltransmission coefficient Ktheory. The “measured” thermal transmissioncoefficient Kactual is ascertained based on the media temperatures andthe size of the heating surface. The theoretical thermal transmissioncoefficient Ktheory is determined, for instance, based on the geometrydata, such as pipe dimension, width separation and/or longitudinalseparation, of the heating surface. The base evaluation factor fbase isdetermined from an operating state deemed to be optimal with basiccontamination present, for example, an acceptance test of the steamgenerator, and is stored. The calculation of the reference stateincludes a recalculation of the steam generator with the basic datastored in the system and certain current process data, such as feedwaterparameters, fresh steam parameters and repeater parameters. Precisedetails of the process data used are not however disclosed.

DE 10 2016 225 528 A1 discloses a method for monitoring a contaminationstate in a heat exchanger with the help of an additional temperaturesensor, which is arranged in or on the heat exchanger wall. Thetemperature sensor detects an operating wall temperature of the heatexchanger. This operating wall temperature is correctively calculatedand a deviation between the correctively calculated operating walltemperature and a reference wall temperature is determined. Thecorrection of the operating wall temperature takes account of changes inmeasured values that occur as a result of operating conditions deviatingfrom reference conditions, for example deviations in the fluidtemperatures or in the volume flows of the fluids. Operating walltemperature and reference wall temperature are values that are measuredat the same point and/or are predetermined for the same point on theheat exchanger.

A current fouling resistance R_(f) can be calculated from the differencebetween a current thermal transmission resistance 1 / k_(actual) and athermal transmission resistance 1/k_(target), which was determined inthe clean state of the heat exchanger:

$R_{f} = {\frac{1}{k_{actual}} - \frac{1}{k_{target}}}$

It has, however, been found that an evaluation of the fouling resistanceon this basis is inaccurate. For example, changes in level of thethermal transmission resistance occur without any apparent particularreason, as would be present, for example, during cleaning or while theheat exchanger is being replaced.

SUMMARY OF THE INVENTION

In view of the foregoing, it is therefore an object of the presentinvention to provide a method and device with which an even moreaccurate determination of fouling in a heat exchanger can occur.

This and other objects and advantages are achieved in accordance withthe invention by a , computer program, device and method in which, inorder to determine fouling, a value for a variable characterizing thefouling is determined from a value for a first variable affected by thefouling and a value of a second variable, where a change in the firstvariable caused by a change in a property of the first and/or of thesecond medium, in particular of a flow of the first and/or of the secondmedium through the heat exchanger, is compensated for at least in partby the second variable.

The variable characterizing the fouling is preferably a thermaltransmission resistance or a thermal transmittance. However, it can alsobe a flow resistance, for example.

The invention is based on the finding that changes in the level of thevariable characterizing the fouling can frequently be explained bychanges in the flow of the first and/or second medium. The reason forthis is that, when there are changes in flow, the flow velocity and theflow type at the points in the thermal transmission can change from thefirst to the second medium. Depending on the flow type that then occurs(for example, laminar flow, weakly turbulent flow, or strongly turbulentflow) and flow velocity this can however also result in changes in thevalue of the first variable affected by the fouling. Even within oneflow type, the mixing and thus the thermal transmission can change as afunction of the flow velocity. For example, a turbulent flow at the edgeregions also forms laminar border layers, the size and thus the effectof which thus, for example, depend on the flow or the flow velocity. Fora more accurate determination of a value of the variable characterizingthe fouling, these changes are therefore taken into account inaccordance with the invention. To this end, a change in the firstvariable caused by a change in a flow of the first and/or second mediumthrough the heat exchanger is compensated for at least in part by thesecond variable. In other words, a change in the flow of the firstand/or second medium causes a corresponding change in the secondvariable, which is then used to compensate for the effect of the changein flow on the first variable. As a result, changes in level of thefirst variable that are calculated from measured data and that until nowhave been inexplicable can be very readily explained and compensatedfor.

In the event of a change in flow, the invention also enables a reliablequantification of the fouling resistance for different heat exchangers.Here, no knowledge of material properties or structural properties ofthe heat exchanger is necessary. The invention operates purely on thebasis of measured data. Instead of using only the thermal transmissionresistance or the thermal transmittance (or the thermal transmissioncoefficient (k value)) or the flow resistance as an indicator of thefouling, the invention uses this variable and at the same time alsointegrates the effect of the flow dynamic of both the media on the finalresult.

In accordance with the invention, it is not the heat flow but thethermal transmission resistance or the thermal transmittance (or athermal transmission coefficient (k value)) or the flow resistance thatis taken into account. As a result, the fouling resistance containedtherein is of advantage regardless of the operating point.

Furthermore, there is no requirement for a model of the heat exchanger,which would have to be laboriously prepared by an expert. All resultsand interim steps can furthermore be represented in 2D or 3Dcharacteristic fields. No abstract multidimensional characteristicfields are required for the calculation.

The invention does not require any special additional measuringinstruments (for example, a temperature sensor on a heat exchangerwall), but gets by with the instrumentation normally present for heatexchangers.

Furthermore, it is also possible to dispense with one of themeasurements of flows and input/output temperatures of the media, sothat not even full instrumentation is required.

If individual process variables of the product medium or service medium,such as the inlet temperature, are determined based on given basicconditions and hence can be accepted as unchanging, they likewise do notneed to be measured.

It is not necessary to detect further variables such as materialproperties of both the media or structural properties of the heatexchanger and thus no provision is made for this either. On thecontrary, the invention assumes that these are not known. Any constantscan be assumed for this, which then when seen in absolute terms resultin false values for the first variable, the second variable and thevariable characterizing the fouling, but ultimately the relative changesin these variables are decisive for the functioning and the success ofthe method. This is also sufficient in practice in most cases.

Using the example of an industrial heat exchanger, a significantlybetter result can be achieved with the invention in the determination offouling than with a conventional calculation. The results can thus helpa plant operator to obtain a significantly better evaluation of thefouling resistance. The invention can advantageously be applied not onlyto the heat balances but also to the consideration of the pressuredifferences and thus of the flow resistances.

A particularly good or optimal compensation of the changes in flow canbe achieved if the second variable is a variable unaffected by thefouling.

The first variable affected by the fouling is, in accordance with afirst alternative embodiment of the invention, a thermal transmissionresistance or a thermal transmittance (or a thermal transmissioncoefficient, frequently also referred to as a “k value”). The thermaltransmission resistance or the thermal transmittance (or the k value)can be determined particularly easily from measured values oftemperatures of the first medium and second medium at an inlet and at anoutlet of the heat exchanger, in each case.

If the heat is transmitted from the first medium to the second mediumthrough a wall, the k value is then, for example, theoretically composedas follows:

$k = \frac{1}{\frac{1}{\alpha 1} + \frac{s_{w}}{\lambda_{w}} + \frac{1}{\alpha_{2}} + R_{f}}$or$\frac{1}{\,_{.}k} = {\frac{1}{\alpha 1} + \frac{s_{w}}{\,_{.}\lambda_{w}} + \frac{1}{\alpha 2} + R_{f}}$

where

-   -   R_(f): fouling resistance (in m²K/W)    -   s_(w): wall thickness (in m))    -   λ_(w): thermal conductivity of the wall (in W/mK)    -   a₁: thermal transmission coefficient from the first medium to        the wall (in W/m²K)    -   a₂: thermal transmission coefficient from the second medium to        the wall (in W/m²K)

Changes in the flow of the first and/or second medium through the heatexchanger may result in changes in the flow velocity and flow type andthus in changes in the thermal transmission coefficient a_(1,2).

Where

$X = {\frac{1}{{\alpha}_{1}} + \frac{1}{\alpha_{2}} + \frac{s_{w}}{\lambda_{w}}}$

this gives

1/k=X+R _(f)

The fouling resistance R_(f) can then be calculated by

R _(f)=1/k−X.

Here, the following apply:

R_(f): the variable characterizing the fouling,

1/k: the first variable,

X: the second variable.

The second variable X is here consequently a variable unaffected by thefouling.

The second variable is preferably thus a measure of the thermaltransmission coefficient between the first medium and the wall, thethermal conductivity of the wall and the thermal transmissioncoefficient between the second medium and the wall.

In accordance with a second embodiment of the invention, the variableaffected by the fouling is a flow resistance of the first or secondmedium through the heat exchanger. A flow resistance can be determinedparticularly easily from measured values of pressures of the first andsecond mediums at an input and at an output of the heat exchanger ineach case.

In accordance with a particularly advantageous first embodiment of themethod (referred to as “Method 1” below) at the time of a change inflow, in particular of an abrupt change, the value of the secondvariable is to this end changed such that the value of the variablecharacterizing the fouling remains constant.

In each case after an initial startup or cleaning of the heat exchanger,i.e., when no fouling is present, an initial value of the first variablecan be determined (or “learned”) and the second variable can be set toan initial value that corresponds to the initial value of the firstvariable. Both the variables then fully compensate one another. If inthe further operation of the heat exchanger the value of the firstvariable increases because of fouling and because of changes in flow,then the changes in flow bring about a corresponding change in thesecond variable, and result in a corresponding compensation of the firstvariable.

This method is particularly suitable for operation of the heat exchangerwith operating phases, in which the flow is in each case piecewiseconstant and then changes abruptly. For example, this corresponds to therelatively common case in which the flow of the product medium isregulated, where the target values for this are predetermined asconstant. A constant change in flow can only be processed in a piecewisemanner. However, a continuous adjustment could then occur via aninterpolation between the piecewise changes. It is advantageous thatchanges in the medium after cleaning have no effect on the result andnor is any learning data required.

In accordance with a particularly advantageous second embodiment of themethod (referred to below as “Method 2”) a function can be defined thatin each case assigns a value for the second variable to a value for aflow through the heat exchanger of the first and/or of the secondmedium.

This function can be determined or “learned” in a time interval after aninitial startup of the heat exchanger or after cleaning the heatexchanger of fouling. The function is preferably formed by a regressionof measured values of the flow and associated values of the secondvariable in the time interval. The regression can, for example, be alinear regression (if only the flow of one of the two media changes) ora 3D regression (if the flows of both media change). This method canalso take account of constant changes and is relatively resistant todeviations in normal operation, but for this also requires severalcleaning operations (and thereafter several different changes in flow)to “train” the function. The method also enables comparisons between thequality of cleaning operations.

In accordance with a particularly advantageous third embodiment of themethod (referred to below as “Method 3”), value ranges are defined forthe flow, to which in each case a value for the second variable isassigned. Here, the assignment of the values of the second variable tothe flow is advantageously determined or “learned” here in a timeinterval after an initial startup of the heat exchanger or aftercleaning the heat exchanger of fouling. The transitions between valuesof the second variable can optionally be somewhat filtered at the rangeboundaries, so that they do not change too sharply. It is also possibleto interpolate between the various learned points, instead ofquantizing, in order to create a “smoother” transition.

The time interval for defining the function or the range by range valueassignments depends on the speed of the fouling processes and may, forexample, be between a few hours (in the case of rapid fouling processes,which result in weekly cleaning of the heat exchanger, for example) anda few days (in the case of slow fouling processes, which result inmonthly cleaning of the heat exchanger, for example).

Combinations and extensions of the three aforementioned methods are alsopossible. For example, Method 1 can always be used when a change in flowoccurs and the step height and compensation height can be taken intoaccount as a new learning point in Method 2 and 3. Thus learning pointsin a contaminated state are also possible.

In accordance with a further advantageous embodiment of the method, acharacteristic curve for a relationship between the second variable andthe flow of one of the two media is determined, where for thedetermination of the characteristic curve in a first step acharacteristic curve of a mathematical derivation of the first variableafter the flow of the medium is determined and, in a second step, thecharacteristic curve contained in the first step is again integratedwith respect to the flow of the medium.

The presently contemplated embodiment of the method makes use of thefact that the variable characterizing the fouling follows a slow andreasonably steady trend. The relationship between the first variable andthe flow thus shifts continually, so that it is not possible to estimatethe relationship directly. The problem therefore exists of estimating acharacteristic curve (static relationship) between two variables.Besides the static relationship, an additive trend also acts on thedependent variable in this case.

The basic idea for solving this problem is to estimate the derivation ofthe first variable after the flow (for example, (d 1/k)/dF)), from whichthe fouling can be subtracted. The integration of the derivation thenagain supplies the actual relationship, the absolute value obviouslybeing lost. This is, however, also not necessary in the application,because only relative changes in flow have to be compensated for.

In a further advantageous embodiment of the method, a firstcharacteristic curve for a relationship between the second variable andthe flow of the first medium and a second characteristic curve for arelationship between the second variable and the flow of the secondmedium are determined at the same time, where for the determination ofthe characteristic curves, in a first step, a characteristic curve of amathematical derivation of the first variable after the flow of therespective medium is determined for each of the two media and, in asecond step, the characteristic curves contained in the first step areagain integrated with respect to the flow of the respective medium.

The presently contemplated embodiment of the method is particularlyadvantageous in the event of simultaneous changes in the flows of bothmedia. Thus, two characteristic curves (static relationships) betweentwo variables each have to be estimated here. Besides the staticrelationships, an additive trend additionally acts on the dependentvariable in this case. Applied to the heat exchanger, the effects ofboth the characteristic curves for the second variable overlap as afunction of the flow of the respective medium.

The advantage of both the last-mentioned embodiments of the method isthat there is no reliance on learning the characteristic curves aftercleaning, because the fouling effect is largely compensated for by theformation of derivations.

It is also an object of the invention to provide a device for theimplementing the disclosed embodiments of the method, where the devicecomprises a further device for receiving measured values or variables ofthe heat exchanger derived therefrom. The device also includes anevaluation device that is configured to determine, from the measuredvalues or the derived variables, a value for a variable characterizingthe fouling from a value for a first variable affected by the foulingand a value of a second variable, where a change in the first variablecaused by a change in a flow of the first medium and/or the secondmedium through the heat exchanger is compensated for at least in part bythe second variable.

The first variable can, in this case, be a thermal transmissionresistance or a thermal transmittance (or a thermal transmissioncoefficient (k value)), where the first variable and the second variableare determined from a plurality of the following measured variables (i)temperatures of the first and second mediums at the inlet and at theoutlet of the heat exchanger and (ii) flows of the first and secondmediums through the heat exchanger, and without using materialproperties of the first medium and second mediums and structuralproperties of the heat exchanger in the determination of the first andthe second variable.

The first variable can, however, also be a flow resistance, wherein thefirst variable and the second variable are determined from a pluralityof the following measured variables (i) pressures of the first andsecond mediums at the inlet and at the outlet of the heat exchanger and(ii) flows of the first and second mediums through the heat exchanger,where the determination of the first and the second variable occurwithout using material properties of the first medium second mediums andstructural properties of the heat exchanger.

The “derived variables” can, for example, be statistical variables suchas mean values, minima, maxima of measured values.

It is also an object of the invention to provide a computer program thatcomprises instructions which, when the program is executed on a computerincluding a processor and memory, cause the computer to execute aninventive method as described above.

A corresponding computer program product comprises a storage medium, onwhich a program containing instructions is stored which, when theprogram is executed on a computer including a processor and memory,cause the computer to execute an inventive method as described above.

Other objects and features of the present invention will become apparentfrom the following detailed description considered in conjunction withthe accompanying drawings. It is to be understood, however, that thedrawings are designed solely for purposes of illustration and not as adefinition of the limits of the invention, for which reference should bemade to the appended claims. It should be further understood that thedrawings are not necessarily drawn to scale and that, unless otherwiseindicated, they are merely intended to conceptually illustrate thestructures and procedures described herein.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention and further advantageous embodiments of the invention areexplained in greater detail below in the figures using exemplaryembodiments, in which:

FIG. 1 shows a block diagram of a heat exchanger and of a device fordetermining fouling in the heat exchanger in accordance with theinvention

FIG. 2 shows a temporal progression of a standardized k value for anindustrial heat exchanger in accordance with the prior art;

FIG. 3 shows a schematic temporal progression of the fouling resistancewithout any change in flow in a calculation in accordance with Method 1of the invention;

FIG. 4 shows a schematic temporal progression of the fouling resistancewith a change in flow in a calculation in accordance with Method 1 ofthe invention;

FIG. 5 shows a temporal progression of the 1/k value for the industrialheat exchanger in accordance with FIG. 1 in a calculation in accordancewith Method 1 of the invention;

FIG. 6 shows an application of a linear regression using the example ofthe industrial heat exchanger in FIG. 2 ;

FIG. 7 shows a temporal progression of the fouling resistance R_(f) forthe industrial heat exchanger in FIG. 2 in a calculation in accordancewith Method 2 of the invention;

FIG. 8 shows a temporal progression of the fouling resistance R_(f) forthe industrial heat exchanger in FIG. 2 in a calculation in accordancewith Method 3 of the invention;

FIG. 9 shows a temporal progression of the correction variable X for theindustrial heat exchanger in FIG. 2 in a calculation in accordance withMethod 4 of the invention;

FIG. 10 shows a temporal progression of flows of a service medium and aproduct medium for an industrial heat exchanger for determination offouling in accordance with a further embodiment of the invention;

FIG. 11 shows a temporal progression of temperatures of the servicemedium and of the product medium in relation to the flows in accordancewith FIG. 10 ,

FIG. 12 shows a temporal progression of a variable characterizing thefouling determined in accordance with Method 5 of the invention from theflows and temperatures in accordance with FIG. 10 and FIG. 11 ;

FIG. 13 shows a temporal progression of flows of a service medium and ofa product medium for an industrial heat exchanger for a determination offouling in accordance with a further embodiment of the invention;

FIG. 14 shows a temporal progression of temperatures of the servicemedium and of the product medium in relation to the flows in accordancewith FIG. 13 ′

FIG. 15 shows a temporal progression of a variable characterizing thefouling determined in accordance with Method 6 of the invention from theflows and temperatures in accordance with FIG. 13 and FIG. 14 ;

FIG. 16 shows a block diagram of a heat exchanger and a Cloud-baseddevice for determining fouling in a heat exchanger in accordance withthe invention; and

FIG. 17 is a flowchart of the method in accordance with the invention.

DETAILED DESCRIPTION OF THE EXEMPLARY EMBODIMENTS

FIG. 1 shows by way of example and in a simplified representation a heatexchanger 1 for the transmission of heat or cold from a service medium Sto a product medium P. The heat exchanger 1 is represented by way ofexample as a reverse current heat exchanger, but other constructions ofheat exchangers are also possible. The product medium P flows through aline 2. In the direction of flow, upstream of the heat exchanger 1, theflow F_(P) (or the flowrate or the volume flow) of the product mediumand its temperature T_(P, In) are measured upstream of the inlet intothe heat exchanger 1 via a flow sensor 4 and a temperature sensor 5. Afurther temperature sensor 6 arranged in the direction of flowdownstream of the heat exchanger 1 measures the temperature T_(P, Out)of the product medium P exiting from the heat exchanger 1.

The product medium P is heated or cooled via a service medium S, whichis supplied to the heat exchanger 1 from a supply of heating or coolant.In the direction of flow, upstream of the heat exchanger 1, the flowF_(S) (or the flowrate or the volume flow) of the service medium and itstemperature T_(S, In) are measured upstream of the inlet into the heatexchanger 1 via a flow sensor 7 and a temperature sensor 8. A furthertemperature sensor 9 arranged in the direction of flow, downstream ofthe heat exchanger 1, measures the temperature T_(S, Out) of the servicemedium S exiting from the heat exchanger 1.

To monitor the heat exchanger 1 for fouling, the flow measured valueF_(P) and the temperature measured values T_(P, In), T_(P, Out) of theproduct medium P and the flow measured value F_(S), as well as thetemperature measured values T_(S, In), T_(S, Out) of the service mediumS, are transferred to a device 10 for determining fouling. If individualprocess variables of the product medium P or of the service medium S,for example, its inlet temperature T_(P, In) or T_(S, In), areestablished based on given basic conditions and hence can be assumed tobe unchanging, they do not need to be measured.

The following applies for the product-related and service-related heatflows {dot over (Q)}_(P) and {dot over (Q)}_(S):

{dot over (Q)} _(P) =c _(P, P)·ρ_(P) ·F _(P)·(TP, _(out) −T _(P, In))

and

{dot over (Q)} _(S) =−c _(P, S)·ρ_(S) ·F _(S)·(T _(S, Out) −T _(S, In)).

Where

c_(P, P) thermal capacity of the product medium,

c_(P, S) thermal capacity of the service medium,

ρ_(P) density of the product medium,

ρ_(S) density of the service medium.

Ignoring losses, the entire amount of heat dissipated from the servicemedium S is transferred to the product medium P, so that both heat flowsare identical ({dot over (Q)}_(P)={dot over (Q)}_(S)={dot over (Q)}).Alternatively, the heat flow can also be calculated using the followingrelationship, which stems from the mechanical structure of the heatexchanger:

{dot over (Q)}=k·A·ΔT _(m).

The following applies here:

k: thermal transmission coefficient (in W/m²K)

A: available surface for heat exchange (in m²)

ΔT_(m): mean logarithmic temperature difference

Q: heat flow.

The mean logarithmic temperature difference ΔT_(m) is defined as:

${{\Delta T_{m}} = \frac{{\Delta T_{A}} - {\Delta T_{B}}}{\ln\left( \frac{\Delta T_{A}}{\Delta T_{B}} \right)}},$

where ΔT_(A) stands for the temperature difference of the inlet side(from the perspective of the product medium) and ΔT_(B) for that of theoutlet side.

Thus, the transferred heat flow can be calculated in three variants, as:

a) heat flow dissipated by Medium 1

{dot over (Q)} _(P) =−c _(P, P)ρ_(P) F _(P) (T _(P, Out) −T _(P, In))

b) heat flow passing through the heat exchanger 1

{dot over (Q)}=k·A·ΔT _(m)

c) heat flow dissipated by Medium 2

{dot over (Q)} _(S) =−c _(P, S)ρ_(S) F _(S)(T _(S, Out) −T _(S, In))

It follows from this that:

c _(P, P)ρ_(P) F _(P)(T _(P, Out) −T _(P, In))=k·A·ΔT _(m) =−c_(P, S)ρ_(S) F _(S)(T _(S, Out) −T _(S, In)).

In general, it is now assumed that the fouling resistance is independentof the operating point. The current fouling resistance can be calculatedfrom the difference between the current thermal transmission resistance1/k_(actual) and the thermal transmission resistance 1/k_(target) thatwas determined in the clean state.

$R_{f} = {\frac{1}{k_{actual}} - \frac{1}{k_{target}}}$$k = \frac{1}{\frac{1}{\alpha_{i}} + \frac{s_{w}}{\lambda_{w}} + \frac{1}{\alpha_{a}} + R_{f}}$

Thus the k value can be calculated using the relationship:

$k = {\overset{.}{Q}\frac{1}{A}\frac{\ln\left( \frac{\Delta T_{A}}{\Delta T_{B}} \right)}{{\Delta T_{A}} - {\Delta T_{B}}}}$

where

ΔT _(A) =T _(P, In) −T _(S, Out) and ΔT _(B) =T _(P, Out) −T _(S, In)

in the case of a reverse current heat exchanger.

In the case of values for A, c_(P, P), c_(P, S), ρ_(P) and ρ_(S)regarded as constant, a relative value for k can thus be correctedmerely with the help of the measured values of the input-side andoutput-side temperatures and of the flows of both the media.

FIG. 2 shows by way of example a typical progression of the 1/k valueover the time t for an industrial heat exchanger. For simplification, ak value k₀ present at the time t₀=0 has been determined, and in FIG. 2 avalue 1/k′ related to the initial value k₀ is represented. Perpendicularlines in this case show the cleaning time points. In some ranges, adissipation of 1/k′ caused by fouling can be identified here. Levelchanges are, however, apparent at the points marked with an arrow, whichmake an accurate evaluation of the fouling resistance more difficult.

As has been found, the determination of the fouling resistance can occurmore accurately by additionally taking changes in flow in the productmedium and/or service medium into account during the evaluation.

If the heat is transmitted from the first medium to the second mediumthrough a wall, the k value is then in theory composed as follows:

$k = \frac{1}{\frac{1}{\alpha 1} + \frac{s_{w}}{\lambda_{w}} + \frac{1}{\alpha_{2}} + R_{f}}$or$\frac{1}{\,k} = {\frac{1}{\alpha 1} + \frac{s_{w}}{\,\lambda_{w}} + \frac{1}{{\alpha}_{2}} + R_{f}}$

where

-   -   R_(f): fouling resistance (in m²K/W)    -   s_(w): wall thickness (in m))    -   λ_(w): thermal conductivity of the wall (in W/mK)    -   a₁: thermal transmission coefficient from the first medium to        the wall (in W/m²K)    -   a2: thermal transmission coefficient from the second medium to        the wall (in W/m²K).

Changes in flow and thus changes in the flow type or within a flow typecan result in changes in the thermal transmission coefficient a_(1,2).

Where

$X = {\frac{1}{{\alpha}_{1}} + \frac{1}{\alpha_{2}} + \frac{s_{w}}{\lambda_{w}}}$

the following is produced:

1/k=X+R _(f).

The fouling resistance R_(f) can then be calculated by:

R _(f)=1/k−X.

In this case

R_(f): is a variable characterizing the fouling,

1/k: is a first variable which is affected by the flow,

X: is a second variable which is not affected by the fouling.

The second variable X is thus a measurement of the thermal transmissioncoefficient between the first medium and the wall, the thermalconductivity of the wall and the thermal transmission coefficientbetween the second medium and the wall.

In accordance with the invention, changes in the first variable causedby changes in flow, here changes in the calculated k value, arecompensated for at least in part with the help of a second variable,here a value of the variable X.

Three methods for how the flow can be taken into account are nowpresented here based on FIGS. 3 to 10 :

Method 1

In Method 1 the value for X is adjusted at each abrupt change in flow.Here, the following assumptions are made:

-   -   the wall thickness and the thermal conductivity thereof        (sw/λw=const.) do not change in operation,    -   the properties of the media do not change, or only        insignificantly,    -   the fouling resistance does not significantly decrease or        increase without a particular reason (for example cleaning) in        normal operation.

In a learning phase, immediately after cleaning, an initial value for Xis learned.

For a certain time interval after cleaning, it can be assumed that thefouling resistance is Rf=0.

In this range, the values for ¹/a₁, 1/a₂ and s_(w)/λ_(w) are learned(aggregated in the value X). Where R_(f)=0 and X=1/a₁+1/a₂+s_(w)/λ_(w),X₀ for the initial interval (or after a cleaning interval) can now bedetermined using the previously calculated k value k₀. X₀=1/k₀ applieshere.

Case 1: The flows do not change

In this case, the values of a also do not change, i.e., X remainsconstant. Each change in the 1/k value can thus be attributed tofouling. The fouling resistance can thus be calculated using therelationship R_(f)=1/k−X. FIG. 3 to this end shows by way of example aprogression of 1/k, X and R_(f) over the time t. The value X is constantand results in a constant difference between 1/k and R_(f).

Case 2: A flow changes at the time t₀

At the time t₀, the fouling resistance R_(f)(t₀) is briefly keptconstant and X_(new) is calculated, for example, withX_(new)=1/k−R_(f)(t₀).

For 1/k a mean value for an interval from t₀ to t₀+x can now be used.Alternatively, X_(new) can also be calculated as follows:

X _(new) =X _(old)−(1/k _(old)−1/k _(new)).

1/kola and 1/knew here stand for an averaged 1/k value in an intervalprior to or after a change in flow. Both approaches show almostidentical results.

In the subsequent progression, the fouling resistance is then calculatedagain using R_(f)=1/k_(new)−X_(new).

FIG. 4 to this end shows by way of example a progression of 1/k, X andR_(f) over the time t. As is apparent, with this method the foulingresistance R_(f) is continued steadily in the event of a change in theflow at the time t₀, instead of resulting in a change in level.

If this method is now used to calculate the 1/k value, X and R_(f) forthe industrial heat exchanger in FIG. 2 and this is plotted over thetime t, the progressions shown in FIG. 5 are produced. Only relativevalues are shown here. Perpendicular lines in this case again show thecleaning times. For simplification, initial values 1/k₀ and X₀ presentat the time t₀=0 have now been determined and values 1/k′ and X′ relatedto these initial values are represented in FIG. 5 .

In the calculation of the 1/k′ value, level changes are again apparentat the points marked with an arrow, but in the calculation of therelative fouling resistance R_(f) are largely compensated for by changesin the X′ value.

This method is particularly suitable for an operation of the heatexchanger with operating phases in which the flow is in each casepiecewise constant and then changes abruptly. A constant change in flowcan only be processed in a piecewise manner. A continuous adjustmentcould then, however, occur via an interpolation between the piecewisechanges. Changes in the medium after cleaning advantageously have noeffect on the result, and nor is any learning data required.

Method 2

As already described, as a rough approximation it can be assumed thatthe fouling resistance after cleaning is ≈0. X(F)=1/k here. This initialinterval is now used for different flows to find a relationship betweenX and F (flow) in the form of a function f. Even if the flow changeswithin this interval. A regression, in particular a linear regression,or even better a nonlinear regression, can be used for this. Acorresponding X value can be calculated for any flows with the result ofthis interpolation.

FIG. 6 shows by way of example an application of the linear regression,using the example of the industrial heat exchanger in FIG. 2 . To createthe linear regression and thus to define the function f, the associatedX values have been determined (marked with “*” in FIG. 6 ) aftercleaning of the heat exchanger for a number of averaged flow valuesF_(P) of the product side. Changes in flow within this interval aretaken into account in this case. The following thus applies: X=f(F_(p)),where the function f is a product of the linear regression of F_(p) andX.

If this method is now used to calculate the relative fouling resistanceR_(f) for the industrial heat exchanger in FIG. 2 and is plotted overthe time t together with the values X determined via the linearregression, the product is a progression shown in FIG. 7 . Forsimplification, the initial value X₀ present at the time t₀=0 has beendetermined here too and a value X′ related to this initial value isrepresented in FIG. 7 .

As is apparent, this method also produces a satisfactory result in manyranges.

Perpendicular lines in this case again show the cleaning times.

The function f can, for example, be formed by a linear regression (ifonly the flow of one of the two media changes, see FIG. 6 ) or a 3Dregression (if the flows of both media change) of measured values offlows and associated values of the second variable in the time intervalafter an initial startup or cleaning. This method can also take accountof constant changes, and is relatively resistant to deviations in normaloperation, but for this also requires a plurality of cleaning operations(and following this a plurality of different flows) to “train” thefunction f. It also enables comparisons between the quality of cleaningoperations.

Method 3

The X values learned after an initial startup or cleaning can be used toform value ranges for the flow. Within such a range each flow value isassigned a learned X value. So that the transitions between two X valuesdo not become too abrupt, this X value can be filtered somewhat overtime.

If this method is now used to calculate the relative fouling resistanceR_(f) and X for the industrial heat exchanger in FIG. 2 and to plot thisresistance over the time t, the product is a progression shown in FIG. 8. For simplification, initial values 1/k₀ and X0 present at the timet₀=0 have been determined and values 1/k′ and X′ related to theseinitial values are shown in FIG. 5 . The calculation was performed usingthe heat quantity of the product side. Perpendicular lines in this caseagain show the cleaning times. As is apparent, this method againproduces a satisfactory result in many ranges.

The assignments of the values of the second variable to the flow areadvantageously determined here in a time interval after an initialstartup of the heat exchanger or after cleaning the heat exchanger offouling. The transitions between values of the second variable canoptionally be somewhat filtered at the range boundaries, so that they donot change too sharply. It is also possible to interpolate between thevarious learned points, instead of quantizing, in order to create a“smoother” transition.

What is known as the “interpolation points method” represents anopportunity for optimization here. This method likewise represents anopportunity for how the analysis of a relationship between flow andreference value could be implemented. To this end, a rough presentationis required of how the characteristic curve of the a value could look asa function of the flow velocity. Basic conditions for the subsequentcharacteristic curve or function could already be found here, such asmonotonicity of the curve. First values for the analysis are obtainedand plotted in the clean state after cleaning operations.

New values are added during the runtime. These are brought together in aparticular range, weighted with the previous values, and thecharacteristic curve is updated. The weighting factor can be the numberof previous points in a range or the current fouling resistance.

In addition to the three methods, combinations and extensions can alsobe applied.

Combination of Methods 1 and 2

This combination could be used to determine the fouling resistance orthe X value for the heat exchanger first with Method 1 and then in themedium term the X value thanks to a ratio between both methods (as afunction, for example, of the deviation between Method 1 and 2, thevariance of Method 2 or the number of data points in Method 2). In thelong term Method 2 alone should then suffice.

Method 4

With the help of Method 1 the X value changes and the changes in flowbefore and after are known in the event of flow changes. The amount ofthe flow change (ΔF₁) and of the X value (ΔX₁) can now firstly becalculated. Thus, for each future (and constant) change in flow, theeffects relative to the previous X value can be calculated. If there isa plurality of usable changes, a linear regression between ΔF₁ and ΔX₁is used. FIG. 9 to this end shows an assignment of values for X to theflow F over the time t.

To work out the final X value, it is possible to interpolate between thedifferent sampling points, in order to avoid an abrupt progression (seedashed line in FIG. 9 ). A combination of Method 1 and Method 4therefore offers particular advantages.

Method 5

In accordance with an embodiment of the method, referred to as Method 5,a characteristic curve for a relationship between the second variableand the flow of one of the two media is determined, where to determinethe characteristic curve, in a first step, a characteristic curve of amathematical derivation of the first variable after the flow of themedium is determined and, in a second step, the characteristic curveobtained in the first step is again integrated with respect to the flowof the medium.

This method makes use of the fact that the variable characterizing thefouling follows a slow and reasonably steady trend. The relationshipbetween the first variable and the flow thus shifts continually, so thatit is not possible to estimate the relationship directly. The problemtherefore exists of estimating a characteristic curve (staticrelationship) between two variables. Besides the static relationship, anadditive trend also acts on the dependent variable in this case.

The basic idea for solving this problem is to estimate the derivation ofthe first variable after the flow (for example, (d 1/k)/dF)), from whichthe fouling can be subtracted. The integration of the derivation thenagain supplies the actual relationship, the absolute value obviouslybeing lost. This is, however, also not necessary in the application,because only relative changes in flow have to be compensated for.

It is assumed that the reciprocal k value is composed of the sum of thefouling resistance and X:

${\frac{1}{k} = {X + R_{f}}},$

where X is composed of all further thermal resistances. The timederivation produces:

$\frac{d\frac{1}{k}}{dt} = {{\frac{dX}{dF}\frac{dF}{dt}} + \frac{{dR}_{f}}{dt}}$${{\kappa(t)} = {{\frac{dX}{dF}{\Phi(t)}} + m}},$

wherein

${{\kappa(t)} = \frac{d\frac{1}{k}}{dt}},{{\Phi(t)} = \frac{dF}{dt}},{m = {\frac{{dR}_{f}}{dt}.}}$

Thus, the following applies:

$\frac{dX}{dF} = \frac{{\kappa(t)} - m}{\Phi(t)}$

For Φ₁(t)≠Φ₂(t), the following applies:

${\frac{1}{\Phi_{1} - \Phi_{2}}\left( {{\Phi_{1}\frac{dX}{dF}} - {\Phi_{2}\frac{dX}{dF}}} \right)} = \frac{dX}{dF}$

At a point X₀, F₀ the unambiguous but unknown relationship

${\frac{dX}{dF}❘}_{X_{0},F_{0}}$

applies, regardless of Φ(t) and κ(t).

Hence the following applies:

$\frac{dX}{dF} = {{\frac{1}{\Phi_{1} - \Phi_{2}}\left( {{\Phi_{1}\frac{dX}{dF}} - {\Phi_{2}\frac{dX}{dF}}} \right)} = {{\frac{1}{\Phi_{1} - \Phi_{2}}\left( {{\Phi_{1}\frac{{\kappa_{1}(t)} - m}{\Phi_{1}(t)}} - {\Phi_{2}\frac{{\kappa_{2}(t)} - m}{\Phi_{2}(t)}}} \right)} = {\frac{1}{\Phi_{1} - \Phi_{2}}\left( {{\kappa_{1}(t)} - {\kappa_{2}(t)}} \right)}}}$

for all Φ₁(t)≠Φ₂(t).

It is therefore necessary to calculate the thus weighted difference inthe

$\frac{1}{k}$

changes, tor two aiiierent changes in flow Φ₁(t)≠Φ₂(t).

To now therefore determine a characteristic curve, it is proposedsuccessively to compile all data with

${\frac{dF}{dt} > c_{F}},$

for all F in the environment of an F₀, and in each case to determine

$\frac{dX}{dF}$

for paired Φ₁(t)≠Φ₂(t). By integrating the derivation characteristiccurve, the characteristic curve that is desired is then created.

In this case, the absolute value is advantageously irrelevant, so thatan initial value need not be taken into account in the integration.

Because of the simpler parameterization the modeling is undertaken onlyqualitatively, i.e., 1/k is determined without exact material data orproperties of the heat exchanger. Thus only relative changes in the kvalue can be calculated. The determined characteristic curves arehowever exactly applicable for relative changes in the flows.

A particular feature of this method is that the actual task ofdetermining the fouling is initially pushed into the background and itis the effect of fouling that is compensated for, in order to estimatethe X-F characteristic curve. Only then is the fouling determined withthe help of the characteristic curve from 1/k. A characteristic curvecan advantageously be easily implemented, so that nothing stands in theway of even an online evaluation.

FIGS. 10 to 12 to this end show a simulation of an industrial heatexchanger with variation in a flow.

FIG. 10 in this case shows a temporal progression of (simulated)measured values of the flow F_(P) of the product medium and of the flowF_(S) of the service medium through the heat exchanger.

FIG. 11 shows the associated (simulated) measured values for thetemperature T_(P, In) of the product medium at the inlet and thetemperature T_(P, Out) of the product medium at the outlet of the heatexchanger. In addition, (simulated) measured values of the temperatureT_(S, In) of the service medium at the inlet and of the temperatureT_(S, Out) of the service medium at the outlet of the heat exchanger areshown.

FIG. 12 shows the associated calculated relative values for 1/k and thefouling resistance R_(f).

In the event of changes in flow, the 1/k value shows a significantdependency, no matter which side of the heat exchanger the changes areon. It is true that an overlaid trend is still apparent in the idealizeddata. Depending on the extent of the fouling, it is not however possibleto derive any reliable information from the 1/k value alone.

By applying the characteristic curves and compensating for theassociated flow dependencies, the estimated fouling progression isproduced (shown offset upward for better visibility). Except for themeasurement noise, a linear trend is apparent. The fouling can thus beascertained very reliably. It should be noted here that at the startboth flows have been changed independently of one another, so that itwas also possible to successively estimate both flow characteristiccurves independently of one another.

Method 6

In accordance with an embodiment of the method referred to as Method 6,a first characteristic curve for a relationship between the secondvariable and the flow of the first medium and a second characteristiccurve for a relationship between the second variable and the flow of thesecond medium are determined, where to determine the characteristiccurves, in a first step, in each case a characteristic curve of amathematical derivation of the first variable after the flow of therespective medium is determined for each of the two media and, in asecond step, the characteristic curves obtained in the first step areagain integrated in respect of the flow of the respective medium.

This method is particularly advantageous in the event of simultaneouschanges in the flows of both media. Thus, two characteristic curves(static relationships) between two variables are each to be estimatedhere. Besides the static relationships, an additive trend additionallyacts on the dependent variable in this case. When applied to the heatexchanger, the effects of both the characteristic curves for the secondvariable overlap one another as a function of the flow of the respectivemedium.

In the case of a heat exchanger, the effects of both the characteristiccurves X_(P)=f_(P)(F_(P)) and X_(S)=f_(S)(F_(S)) on the 1/k valueoverlap one another where

$\frac{1}{k} = {X_{P} + X_{S} + {R_{f}.}}$

The derivation of 1/k after the time produces

$\frac{d\frac{1}{k}}{dt} = {{\frac{dX}{{dF}_{p}}\frac{{dF}_{p}}{dt}} + {\frac{dX}{dF_{S}}\frac{dF_{S}}{dt}} + \frac{dR_{f}}{dt}}$

where X=X_(P)+X_(S).

n_(P) interpolation points (dx_(pi), F_(pi)) of the derivationcharacteristic curve

$\frac{{dX}_{P}}{{dF}_{P}} = {\overset{-}{f_{P}}\left( F_{P} \right)}$

and n_(S) interpolation points (dx_(si), F_(si)) of the derivationcharacteristic curve

$\frac{{dX}_{S}}{{dF}_{S}} = {\overset{¯}{f_{S}}\left( F_{S} \right)}$

are now sought.

To this end, for each time t for which

$\frac{{dF}_{P}}{dt} > {{dFpLimit}{or}\frac{{dF}_{S}}{dt}} > {dFsLimit}$

applies, an equation with three unknowns (dx_(pi),dx_(si),m) isgenerated:

$\frac{d\frac{1}{k}}{dt} = {{dx_{Pi}\frac{dF_{P}}{dt}} + {dx_{Si}\frac{dF_{S}}{dt}} + m}$

n_(D), equations can then be combined in matrix notation, where therespective flow has to be taken into account for the interpolationpoints. Thus the following applies:

Ab = c$\left. {{{{{{{{{b = \left\lbrack \frac{dX_{P}}{dF_{P}} \right.}❘}_{F_{P_{1}}},\ldots,\frac{dX_{P}}{dF_{P}}}❘}_{F_{P_{n_{p}}}},\frac{dX_{S}}{dF_{S}}}❘}_{F_{s_{1}}},\ldots,\frac{dX_{S}}{dF_{S}}}❘}_{F_{s_{n_{s}}}},m} \right\rbrack^{T}$c = [κ(t₁)…κ(t_(m))] A ∈ R^(n_(D) × (n_(p) + n_(s) + 1))

For better understanding, a row of A is specified. At the correspondingtime, it should be the case that F_(P)≈F_(P5) and F_(S)≈F_(S7), wheren_(P)=10 and n_(S)=20. The row of A then corresponds to:

$\left. {{{{\left\lbrack {0,\ldots,0,\frac{dX_{P}}{dF_{P}}} \right.❘}_{F_{P5}},0,{\ldots 0},\frac{dX_{S}}{dF_{S}}}❘}_{F_{S7}},0,\ldots,{0,1}} \right\rbrack^{T}$

where there are entries different from zero only in the 5^(th) and17^(th) (=10+7) and last column.

If the measured values present now cover all flow ranges on the serviceand product side, then there is at least one data point in each columnof A. Assuming that A has the maximum ranking, the equation system canbe resolved in accordance with the unknown in the vector b, such as viaa pseudoinverse.

The two derivation characteristic curves can then again be generatedfrom the vector and integrating these produces the characteristic curvesX_(P)=f_(P)(F_(P)) and X_(S)=f_(S)(F_(S)).

If both characteristic curves are present, then the fouling can beestimated, by first determining 1/k, and the fouling is calculated byapplying the characteristic curves:

$R_{f} = {\frac{1}{k} - X_{P} - X_{S}}$

As already outlined in brief, the absolute values of the characteristiccurves are unknown by the integration. Because of the simplerparameterization, the modeling is in any case implemented onlyqualitatively, i.e., 1/k is determined without precise material data orproperties of the heat exchanger. Thus, only relative changes in the kvalue can be calculated. The determined characteristic curves can,however, be applied precisely for relative changes in the flows.

Here, the actual task of determining the fouling is also initiallypushed into the background and it is the effect of fouling that iscompensated for, in order to estimate both the X-F characteristiccurves. Only then is the fouling determined with the help of thecharacteristic curves from 1/k. Characteristic curves can advantageouslybe easily implemented, so that an evaluation can even be carried outonline.

FIGS. 13-15 to this end show a simulation of an industrial heatexchanger with variation in the flows.

FIG. 13 in this case shows a temporal progression of (simulated)measured values of the flow F_(P) of the product medium and of the flowF_(S) of the service medium through the heat exchanger.

FIG. 14 shows the associated (simulated) measured values for thetemperature T_(P, In) of the product medium at the inlet and thetemperature T_(P, Out) of the product medium at the outlet of the heatexchanger. In addition, (simulated) measured values of the temperatureT_(S, In) of the service medium at the inlet and the temperatureT_(S, Out) of the service medium at the outlet of the heat exchanger areshown.

FIG. 15 shows the relative values calculated therefrom for 1/k and thefouling resistance R_(f).

The 1/k value shows a significant dependency in the case of changes inflow, no matter which side of the heat exchanger said changes are on. Itis true that an overlaid trend is still apparent in the idealized data.Depending on the extent of the fouling, it is not however possible toderive any reliable information from the 1/k value alone. By applyingthe characteristic curves and compensating for the associated flowdependencies, the estimated fouling progression Rf is produced. Exceptfor the measurement noise, a linear trend is apparent. The fouling canthus be determined very reliably, even if both flows change at the sametime.

The same methods can in principle also be transferred to theconsideration of the pressure difference. The flow resistance alsoincreases in the case of fouling, but also depends on the flow.

The disclosed embodiments of the methods enable a reliablequantification of the fouling resistance for different heat exchangerseven in the event of a change in flow. In this case, no knowledge ofmaterial properties or structural properties of the heat exchanger isnecessary. The disclosed embodiments of the method all work purely onthe basis of data. Hitherto, only the pure k value has been used as anindicator for fouling. The disclosed embodiments of the method use thisvariable and at the same time also incorporate the effect of the flowdynamic of both the media into the final result.

Furthermore, there is no requirement for a model of the heat exchanger,which would have to be laboriously prepared by an expert. All resultsand interim steps can furthermore be represented in 2D or 3Dcharacteristic fields. No abstract multidimensional characteristicfields are required for the calculation. Furthermore, it is alsopossible to dispense with one of the measurements F_(P), F_(S),T_(P, In), T_(P, Out), T_(S, In), T_(S, Out), so that fullinstrumentation is not required. If a compensation takes place withrespect to changes in the flow of both media, then it should beunderstood only one temperature measurement can be dispensed with inthis case.

Using the example of an industrial heat exchanger, it was possible toachieve a significantly better result with these disclosed embodimentsof the methods in the determination of fouling than with a conventionalcalculation. The results could thus help a plant operator to obtain asignificantly better evaluation of the fouling resistance. The methodscan advantageously be applied not only to the heat balances but also tothe consideration of the pressure differences and thus of the flowresistances.

The inventive embodiments of the method can be provided as a standaloneapplication in a processing system or can be integrated into a processcontrol system of a processing system. It can also be provided in alocal or remote computer system (“Cloud”), for example by a serviceprovider as “Software as a Service”.

An inventive device 10 for determining fouling shown by way of examplein FIG. 1 comprises a device 20 for receiving the measured valuesT_(P, In), T_(P, Out), T_(S, In), T_(S, Out), F_(P), F_(S) of the heatexchanger 1 and an evaluation device 30 which is configured to determineand output a value for the fouling resistance R_(f) from these measuredvalues via a method in accordance with the disclosed embodiments.Additionally or alternatively the evaluation device can also act as amonitoring device: it can monitor the determined fouling resistance tosee whether a threshold value has been exceeded and if this thresholdvalue is exceeded can thn emit a signal, which for example signals aneed for cleaning.

To this end, the evaluation device 30 comprises a processor unit 31, amemory 32 for storing the received measured data, and a memory 33 inwhich a program 34 containing instructions is stored, which whenexecuted via the processor unit 31 executes the method in accordancewith the disclosed embodiments. The processor unit 31 stores themeasured values M received by the device 20 in the memory 32.

It is not necessary to detect further variables, such as c_(P, P),c_(P, S), ρ_(P), ρ_(S). On the contrary, the disclosed embodiments ofthe method assumes that these are not known. Any constants can beassumed, which then when seen in absolute terms result in a false value,but ultimately the relative changes in this k-value are decisive for thefunctioning and the success of the method in accordance with disclosedembodiments.

The device 10 shown in FIG. 1 can, for example, be provided as astandalone application in a processing system or can be integrated intoa process control system of a processing system.

A device 100 shown in FIG. 16 for determining fouling can in contrast beprovided by a local or remote computer system (“Cloud”), for example, inorder to offer the determination of fouling by a service provider as“Software as a Service”. The receiving device 20 is, in this case,located in situ in the processing system of the heat exchanger 1 and theevaluation device 30 is located on a local or remote computer system(“Cloud”). To this end, the receiving device 20 stores the receivedmeasured values in a memory 21 and sends the measured values M (orvariables derived therefrom) to the evaluation device 30 (for example,at regular intervals in time, on an event-driven basis or on request bythe evaluation device 30) via a transmission device 22, such as over theInternet or an intranet.

The evaluation device 30 comprises a processor unit 31, a memory 32 forstoring the received measured data, and a memory 33, in which a program34 containing instructions is stored, which when executed via theprocessor unit 31 executes the method in accordance with disclosedembodiments of the invention.

The processor unit 31 stores the measured values M received from thedevice 20 via an interface 36 in the memory 32, and where appropriatefor further input variables that are received via a separate interface37. The values for the fouling resistance R_(f) determined with theprogram 34 and/or a signal that signals a need for cleaning are outputvia an interface 38. The interfaces 36, 37 and 38 can in this case alsobe provided by a single shared interface, for example, to the Internetor an intranet.

FIG. 17 is a flowchart of the method for determining fouling in a heatexchanger 1, in which heat from a first medium S is transferred to asecond medium P.

The method comprises determining a value for a variable characterizingthe fouling Rf from a value for a first variable k affected by thefouling and from a value of a second variable X, as indicated in step1710.

Next, a change in the first variable k caused by a change in a flow FS,FP of either the first medium S and/or the second medium P through theheat exchanger 1 is compensated for at least in part by the secondvariable X, as indicated in step 1720.

In accordance with the method of the invention, the first variable k iseither a thermal transmission resistance, a thermal transmittance or athermal transmission coefficient k value, where the first variable k andthe second variable X are determined from measured values of a pluralityof the measured variables comprising (i) temperatures TP, In, TP, Out,TS, In, TS, Out of the first medium S and the second medium P at aninlet and at an outlet of the heat exchanger 1 and (ii) flows FP, FS ofthe first medium S and the second medium P through the heat exchanger 1,and where the determination of the first and the second variable occurswithout using material properties of the first medium S and the secondmedium P and structural properties of the heat exchanger 1.

Thanks to virtually realtime detection of the measured values andcalculation of the fouling resistance a continuous running data-basedfouling analysis and monitoring of the fouling can take place,accompanying the operation of the plant or of the heat exchanger.However, an offline fouling analysis with a time offset to the realoperation of the plant is also possible.

Thus, while there have been shown, described and pointed out fundamentalnovel features of the invention as applied to a preferred embodimentthereof, it will be understood that various omissions and substitutionsand changes in the form and details of the methods described and thedevices illustrated, and in their operation, may be made by thoseskilled in the art without departing from the spirit of the invention.For example, it is expressly intended that all combinations of thoseelements and/or method steps which perform substantially the samefunction in substantially the same way to achieve the same results arewithin the scope of the invention. Moreover, it should be recognizedthat structures and/or elements and/or method steps shown and/ordescribed in connection with any disclosed form or embodiment of theinvention may be incorporated in any other disclosed or described orsuggested form or embodiment as a general matter of design choice. It isthe intention, therefore, to be limited only as indicated by the scopeof the claims appended hereto.

1.-16.
 17. A method for determining fouling in a heat exchanger, inwhich heat from a first medium is transferred to a second medium, themethod comprising: determining a value for a variable characterizing thefouling from a value for a first variable affected by the fouling andfrom a value of a second variable; and compensating for a change in thefirst variable caused by a change in a flow of at least one of (i) thefirst medium and (ii) the second medium through the heat exchanger atleast in part by the second variable, the first variable being one of athermal transmission resistance, a thermal transmittance and a thermaltransmission coefficient, the first variable and the second variablebeing determined from measured values of a plurality of the measuredvariables comprising (i) temperatures of the first medium and the secondmedium at an inlet and at an outlet of the heat exchanger and (ii) flowsof the first medium and the second medium through the heat exchanger,and the determination of the first and the second variable occurringwithout using material properties of the first medium and the secondmedium and structural properties of the heat exchanger.
 18. A method fordetermining fouling in a heat exchanger, in which heat is transferredfrom a first medium to a second medium, the method comprising:determining a value for a variable characterizing the fouling from avalue for a first variable affected by the fouling and from a value of asecond variable; and compensating for a change in the first variablecaused by a change in a flow of at least one of (i) the first medium and(ii) the second medium through the heat exchanger at least in part bythe second variable, the first variable being a flow resistance, and thefirst variable and the second variable being determined from measuredvalues of a plurality of measured variables comprising (i) pressures ofthe first medium and the second medium at an inlet and at an outlet ofthe heat exchanger and (ii) flows of the first medium and the secondmedium through the heat exchanger, and the determination of the firstand the second variable occurring without utilizing material propertiesof the first medium and the second medium and structural properties ofthe heat exchanger.
 19. The method as claimed in claim 17, wherein at atime of a change in flow, the value of the second variable is changedsuch that the value of the variable characterizing the fouling remainsconstant.
 20. The method as claimed in claim 18, wherein at a time of achange in flow, the value of the second variable is changed such thatthe value of the variable characterizing the fouling remains constant.21. The method as claimed in claim 19, wherein after an initial startupand after a cleaning operation of the heat exchanger an initial value ofthe first variable is determined in each case and the value of thesecond variable is set to an initial value which corresponds to theinitial value of the first variable.
 22. The method as claimed in claim17, wherein a function is defined which in each case assigns a value forthe second variable to a value for a flow of at least one of the firstmedium and the second medium.
 23. The method as claimed in claim 22,wherein the function is determined in a time interval after an initialstartup or after cleaning the heat exchanger of fouling.
 24. The methodas claimed in claim 22, wherein the function is formed by a regressionof measured values of the flow and associated values of the secondvariable in the time interval.
 25. The method as claimed in claim 23,wherein the function is formed by a regression, in particular a linearor a 3D regression, of measured values of the flow and associated valuesof the second variable in the time interval.
 26. The method as claimedin claim 24, wherein the regression comprises a linear or a 3Dregression.
 27. The method as claimed in claim 25, wherein theregression comprises a linear or a 3D regression.
 28. The method asclaimed in claim 17, wherein value ranges for the flow are defined, toeach of which a value for the second variable is assigned.
 29. Themethod as claimed in claim 28, wherein assignments of the values of thesecond variable to the flow are determined in a time interval after aninitial startup or after cleaning the heat exchanger of fouling.
 30. Themethod as claimed in claim 17, wherein a characteristic curve for arelationship between the second variable and the flow of one of the twomedia is determined; and wherein, for the determination of thecharacteristic curve, a characteristic curve of a mathematicalderivation of the first variable after the flow of the medium isinitially determined and the characteristic curve initially obtained issubsequently again integrated with respect to the flow of the medium.31. The method as claimed in claim 17, wherein a first characteristiccurve for a relationship between the second variable and the flow of thefirst medium and a second characteristic curve for a relationshipbetween the second variable and the flow of the second medium aresimultaneously determined; and wherein for the determination of thecharacteristic curves for each of the first and second media acharacteristic curve of a mathematical derivation of the first variableafter the flow of the respective first and second medium are eachdetermined and the characteristic curves initially obtained aresubsequently again integrated with respect to the flow of the respectivemedium.
 32. The method as claimed in claim 17, wherein the variablecharacterizing the fouling is a thermal transmission resistance.
 33. Themethod as claimed in one claim 17, wherein only relative changes in thevariable characterizing the fouling, the first variable and the secondvariable are determined.
 34. A device for determining fouling in a heatexchanger, in which heat from a first medium is transferred to a secondmedium, the device comprising: a further device for receiving measuredvalues or variables derived therefrom of the heat exchanger; and anevaluation device which is configured to determine from the receivedmeasured values or the derived variables a value for a variablecharacterizing the fouling from a value for a first variable affected bythe fouling and from a value of a second variable; wherein a change inthe first variable caused by a change in a flow of at least one of (i)the first medium and (ii) the second medium through the heat exchangeris compensated for at least in part by the second variable; and whereinthe first variable and the second variable are determined from measuredvalues of a plurality of measured variables comprising (i) temperaturesof the first medium and the second medium at an inlet and at an outletof the heat exchanger and (ii) flows of the first medium and the secondmedium through the heat exchanger, and the determination of the firstand the second variable occurring without utilizing material propertiesof the first medium and the second medium and structural properties ofthe heat exchanger being utilized.
 35. The device for determiningfouling in a heat exchanger, in which heat is transferred from a firstmedium to a second medium, the device comprising: a further device forreceiving measured values or variables derived therefrom of the heatexchanger; and an evaluation device which is configured to determinefrom the measured values or the derived variables a value for a variablecharacterizing the fouling from a value for a first variable affected bythe fouling and from a value of a second variable; wherein a change inthe first variable caused by a change in a flow of at least one of (i)the first medium and (ii) the second medium through the heat exchangeris compensated for at least in part by the second variable; wherein thefirst variable is a flow resistance; wherein the first variable and thesecond variable are determined from measured values of a plurality ofmeasured variables comprising (i) pressures of the first medium and thesecond medium at an inlet and at an outlet of the heat exchanger and(ii) flows of the first medium and of the second medium through the heatexchanger, and the determination of the first and the second variablesoccurring without utilizing material properties of the first medium andthe second medium and structural properties of the heat exchanger.
 36. Acomputer program comprising instructions which, when executed by aprocessor of a computer, cause the computer to execute the method asclaimed in claim
 17. 37. A computer program comprising instructionswhich, when executed by a processor of a computer, cause the computer toexecute the method as claimed in claim 18.